Theory and application of asymptotic numerical method for the incompressible viscous flows

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A new artificial compressibility method for the incompressible Navier-Stokes equations is developed. This method is Poisson free and provides a suitable algorithm for the parallel computations. Comparisons are made with various existing methods and its performance is shown to be well suited for practical engineering problems with complex geometries. It is theoretically shown that the lattice Boltzmann method essentially solves the same PDE system that the present artificial compressibility method does. The capabilities of these methods are nearly identical and no outcome of the kinetic formulation in the lattice Boltzmann method is found in the present study.